Dynamical spin properties in helical Luttinger liquids Maura - PowerPoint PPT Presentation

Dynamical spin properties in helical Luttinger liquids Maura Sassetti in collaboration with Giacomo Dolcetto, Niccolò Traverso, Fabio Cavaliere, Matteo Biggio Dipartimento di Fisica, Università di Genova Firenze 28/05/2014

Outline Introduction to helical liquids • Rashba quantum wires • Topological insulators Spin properties in helical finite systems • Confinement: helical 1D quantum dot • Peculiar spin textures

Spinfull electrons in a 1D quantum wire

Helical 1D system

Helical 1D system spin-momentum locking! right-moving spin up; left-moving spin down

Helical 1D system spin-momentum locking! right-moving spin up; left-moving spin down Topological protection from backscattering in the presence of TRS T= 1

Realizations Spin-orbit coupled quantum wires in magnetic fields Edge states in two-dimensional topological insulators CdTe HgTe CdTe

Spin-orbit interaction in semiconductor quantum wire (InSb, InAs, GaAs/AlGaAs) Rashba spin-orbit interaction Zeeman coupling

Spin-orbit interaction in semiconductor quantum wire (InSb, InAs, GaAs/AlGaAs) Rashba spin-orbit interaction Zeeman coupling Spin up Spin down [Streda, Seba PRL (2003); Pershin Nesteroff, Privman PRB (2004); Zhang et al. PRB (2006); Quay et al., Nature Physics (2010); Meng Loss PRB (2013)…….]

Spin up Spin down 2 Fermi points right moving spin up, left moving spin down: helical liquid! Experimental detection [C. H. L. Quay et al., Nature Physics (2010)]

Edge states of 2D topological insulators HgTe/CdTe QWs CdTe HgTe CdTe [B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Science 314 , 1757 (2006)]

Two-dimensional topological insulators CdTe HgTe CdTe

Two-dimensional topological insulators CdTe HgTe CdTe Insulating bulk states, gapless counterpropagating edge states connected by time reversal symmetry with spin-momentum locked [B.A.Bernevig, T. L. Hughes, and S.-C. Zhang, Science 314 , 1757 (2006); B.A. Bernevig, SC Zhang PRL (2006); L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83 , 1057 (2011)]

Experimental observation of the QSH effect CdTe CdTe HgTe HgTe CdTe CdTe [Konig et al., Science (2007)]

Why are helical liquids useful? • Spintronics : spin manipulation, spin current generation [Roth et al. Science (2009); Dolcini PRB (2011); Citro, Romeo, Andrei PRB (2001); Sukhanov, Sablikov J.Phys Cond Matt (2012); Dolcetto et al. PRB (2013); Michetti Trauzettel APL (2013); Ferrarro et al PRB (2013)……] • Realizations of Majorana fermions in solid state devices helical unpaired Majorana fermions on opposite edges of the helical wire [Kitaev Phys. Usp (2001); Oreg, Refael, von Oppen, PRL (2010); Lutchyn, Sau, Das Sarma PRL (2010); Alicea Rep Prog Phys (2012) (review); Mourik et al. Science (2012) (exp )……..]

Spin textures in finite size helical systems G. Dolcetto, N. Traverso, M. Biggio, F. Cavaliere, M.S. PRB 87, 235423 (2013); G. Dolcetto, N. Traverso, M. Biggio, F. Cavaliere, M.S. RRL 7, 1059 (2013); G. Dolcetto, F. Cavaliere, M.S. PRB 89, 125419 (2014)

Wigner density oscillations in finite 1D spinfull wires Strong interactions Weak interactions Finite size Friedel oscillations N=6 Wigner cristallization K. Jauregui et al., EPL(1993); S.H. Abendipour et al. .PRA (2007); G.A. Fiete RMP (2007); A. Secchi, M. Rontani PRB (2009) (2010); N. Traverso, F. Cavaliere, M. S., PRB (2011), PRB (2012), NJ.P (2013)

Finite size helical edge Confinement with magnetic barriers breaking time reversal simmetry possible spin flip processes incident trasmitted reflected

Finite size helical edge Confinement with magnetic barriers breaking time reversal simmetry possible spin flip processes incident trasmitted reflected

confined helical 1D quantum island - dependent boundary conditions

Finite size helical 1D Luttinger liquid Interaction term

Diagonalization plasmon modes with velocity electron interaction parameter

Diagonalization plasmon modes with velocity electron interaction parameter Electron field bosonization

Spin density components thermal averages

Exact evaluation of spin averages via bosonization technique Oscillating term related to the number LL power-law envelope function of particles inside the island

Peculiar spin-density oscillating patterns driven by the magnetization angle

Peculiar spin-density oscillating patterns driven by the magnetization angle Difference of half an oscillation! e/2 topological background charge inside the helical island [Qi et al ., Nat Phys 08;Meng et al ., PRL 12]14

G. Dolcetto, N. Traverso, M. Biggio, F. Cavaliere, M.S. PRB 87, 235423 (2013)

Spin-resolved correlation functions for spin states Probability of founding two electrons with spin + in the x- direction at relative distance x weak interactions: uncorrelated liquid state g=0.9 medium interactions g=0.55 strong interactions g=0.25 spin correlated state Marked peaks for strong interactions tendency towards spin ordering G. Dolcetto, N. Traverso, M. Biggio, F. Cavaliere, M.S. RRL (2013)

Conclusions Peculiar spin properties in finite helical systems

Conclusions Peculiar spin properties in finite helical systems Non-equilibrium spin properties (not shown) • Magnetic AC control of the spin textures in a helical LL [G. Dolcetto, F. Cavaliere, M.S, PRB 89, 125419 (2014) ] • Spin pumping in helical systems [Ferraro, Dolcetto, Romeo, Citro, M.S. PRB 87, 085425 (2013)]